Pushing the boundaries of thethermal conductivity of materials

David G. Cahill,C. Chiritescu, Y.-K. Koh, Xuan Zheng

Materials Research Lab and Department of Materials Science, U. of Illinois

N. Nguyen, D. Johnson

Department of Chemistry, U. of Oregon

Pawel Keblinski

Department of Materials Science, RPI

supported by ONR and AFOSR

Outline

• Thermal conductivity and interface thermal conductance.

• Advances in time-domain thermoreflectance.

• Amorphous limit to the thermal conductivity of materials.

• Ultralow thermal conductivity: beating the amorphous limit in nanolaminates and disordered layered crystals.

50 nm

Interfaces are critical at the nanoscale

• Low thermal conductivity in nanostructured materials

– improved thermoelectric energy conversion

– improved thermal barriers

• High thermal conductivity composites and suspensions

Interfaces are critical at the nanoscale

• High power density devices

– solid state lighting– high speed and

power electronics– nanoscale sensors

Micrograph of tunneling magnetoresistive sensorfor 120 GB drives, M. Kautzky (Seagate)

Thermal conductivity and interface thermal conductance

• Thermal conductance (per unit area) G is a property of an interface

• Thermal conductivity Λ is a property of the continuum

Thermal conductivity and interface thermal conductance

• Both properties are difficult to understand and control because they are integral properties.

• For example, simplest case of thermal conductivity where resistive scattering dominates

Λ = 1/3∫ C(ω) v(ω) l(ω) dω

C(ω) = heat capacity of phonon mode

v(ω) = group velocity

l(ω) = mean-free-path

Brief introduction to thermoelectric materials

• Solid-state heat pump; thermal efficiency governed by the “figure of merit” ZT

2S TZT σ=

Λ

S = Seebeck coefficientσ = electrical conductivityΛ = thermal conductivity

Lon Bell, Science (2008)

Brief introduction to thermoelectric materials

• … or write ZT in a more obviously dimensionless form…

Λ = Λlattice + Λelectronic

Λelectronic = LσT

( )2 1

1 /lattice electronic

SZTL

⎛ ⎞= ⎜ ⎟ + Λ Λ⎝ ⎠

Snyder, Caltech, http://thermoelectrics.caltech.edu

Carbon nanotubes

• Evidence for the highest thermal conductivity any material (higher conductivity than diamond)

Yu et al. (2005)

Maruyama (2007)

Can we make use of this?

• Much work world-wide:

– thermal interface materials

– so-called "nanofluids" (suspensions in liquids)

– polymer composites and coatings

Fischer (2007)

Lehman (2005)

Critical aspect ratio for a fiber composite

• Isotropic fiber composite with high conductivity fibers (and infinite interface conductance)

• But this conductivity if obtained only if the aspect ratio of the fiber is high

Critical aspect ratio of a fiber composite

Time domain thermoreflectance since 2003

• Improved optical design• Normalization by out-of-

phase signal eliminates artifacts, increases dynamic range and improves sensitivity

• Exact analytical model for Gaussian beams and arbitrary layered geometries

• One-laser/two-color approach tolerates diffuse scattering

Clone built at Fraunhofer Institute for Physical Measurement, Jan. 7-8 2008

psec acoustics andtime-domain thermoreflectance

• Optical constants and reflectivity depend on strain and temperature

• Strain echoes give acoustic properties or film thickness

• Thermoreflectance gives thermal properties

Time-domain Thermoreflectance (TDTR) data for TiN/SiO2/Si

• reflectivity of a metal depends on temperature

• one free parameter: the “effective”thermal conductivity of the thermally grown SiO2 layer (interfaces not modeled separately)

SiO2

TiN

Si

Windows software

author: Catalin Chiritescu, users.mrl.uiuc.edu/cahill/tcdata/tdtr_m.zip

TDTR: Flexible, convenient, and accurate

• ...with 3 micron resolution…

Thermal conductivity map of a human tooth

www.enchantedlearning.com/ Distance from the DEJ (μm)

-400 -200 0 200

ΛC

/C0

(W m

-1 K

-1)

0.0

0.5

1.0

1.5

2.0

dentin enamel

0

1

2

3

100 μm

Nanotubes in surfactant in water: Transient absorption

• Optical absorption depends on temperature of the nanotube

• Assume heat capacity is comparable to graphite

• Cooling rate (RC time constant) gives interface conductance

G = 12 MW m-2 K-1

Nanotubes in surfactant in water

Critical aspect ratio for a fiber composite

• Isotropic fiber composite with high conductivity fibers (and infinite interface conductance)

• But this conductivity if obtained only if the aspect ratio of the fiber is high

Critical aspect ratio of a fiber composite

• Troubling question: Did we measure the relevant value of the conductance?

"heat capacity G" vs. "heat conduction G"

nanotube/alkane

W/Al2O3

Au/water

PMMA/Al2O3

Interface thermal conductance: Factor of 60 range at room temperature

L = Λ/GΛ = 1 W m-1 K-1

Can we beat the amorphous limit of the thermal conductivity Λmin with interfaces?

• Einstein (1911): random walk of thermal energy

• Not good for crystals: Debye (1914)

• but does work for amorphous solids, Birch and Clark (1940); Kittel (1948)

• and crystals with strong atomic-scale disorder, Slack (1979); Cahill and Pohl (1988).

Einstein (1911)

• coupled the Einstein oscillators to 26 neighbors

• heat transport as a random walk of thermal energy between atoms; time scale of ½ vibrational period

• did not realize waves (phonons) are the normal modes of a crystal

Works well for homogeneous disordered materials

disordered crystal

amorphous

50 nm

Ultralow thermal conductivity in W/Al2O3nanolaminates (Costescu, 2004)

• Thermal conductance of interfaces between dissimilar materials can produce thermal conductivities below the amorphous limit.

W/Al2O3 nanolaminates

W/Al2O3 nanolaminates

• ultra-low conductivity in nanoscale metal/ceramic multilayers

• data close to theoretical prediction of the diffuse-mismatch model (DMM) times layer spacing

Layered disordered crystals: WSe2 by “modulated elemental reactants”

• Deposit W and Se layers at room temperature on Si substrates

• Anneal to remove excess Se and improve crystallinity

• Characterize by RBS, x-ray diffraction (lab sources and Advanced Photon Source) and TEM

Cross-sectional TEM of 60 nm thick WSe2

Seongwon Kim and Jian Min Zuo

Thermal conductivity of WSe2

• 60 nm film has the lowest thermal conductivity ever observed in a fully dense solid. Only twice the thermal conductivity of air.

• A factor of 6 less than the calculated amorphous limit for this material.

Ion irradiation of WSe2

• Heavy ion irradiation (1 MeV Kr+) of 24 nm WSe2 film.

• Novel behavior: ion damage causes the thermal conductivity to increase.

MD simulation of 1 MeV Kr impact on Au

Digression: ion bombardment of a superlattice (with Y. Cao and D. Jena)

• 2.3 MeV Ar ion irradiation of GaN and (AlN)4 nm-(GaN)5 nm

• Lines are Debye-Callaway models assuming phonon Rayleigh scattering scales linearly with ion dose.

• Fit gives Γ = 1 at an ion dose of 1014 cm-2

1012 1013 10142

10

30

100

SL

Λ (W

m-1 K

-1)

Dose (cm-2)

GaN

Molecular dynamics simulation

• MD work by Bodapati and Keblinski (RPI)

• Original LJ model of WSe2 gives 0.06 W/m-K independent of length-scale

• Conclusion: physics is general, not specific to some detail of the WSe2 bonding or microstructure

Conclusions from theoretical work (Hu and Keblinski, unpublished)

• Analysis of the participation ratio: phonon localization is not significant.

• Analysis of mode polarization: incoherent grain boundaries create diffusive but non-propagating vibrational modes. (stacking faults are not sufficient)

• Key to ultralow thermal conductivity is disorder in combination with anisotropy, i.e., an “anisotropic glass”.

• Interface resistance between 2D crystalline sheets? Lowering of the effective density of states for modes diffusing perpendicular to the sheets?

Back to experiment: Can we lower the conductivity even further?

• Synthesize misfit layered compounds by elemental reactants method (Johnson and co-workers) – WSe2/PbTe– MoSe2/PbTe

• Interface density does not matter. Conductivity determined by composition not interface density.

0.0 0.2 0.4 0.6 0.8 1.0PbSe content

0.1

Λ(W

m-1

K-1

)

(PbSe)m : (MoSe2)n

0.03

0.3

(1;5)(1;3)

(1;2)

(2;3)

(2;2)(3;3)(1;1)

(2;1) (3;1)(4.5;1)

Contrast with typical behavior of a superlattice (with Y. Cao and D. Jena)

(AlN)4 nm-(GaN)h

2 10 100 10002

10

100200

η = 1.2 nm50

20

ΛBulkGaN

1 /h vτ − =

GTiN/MgO

Λ (W

m-1 K

-1)

hGaN (nm)

5

Conclusions

• Difficult to take advantage of superlative properties of carbon nanotubes because of "thermally weak" interfaces.

• Can beat the amorphous limit to the thermal conductivity with high densities of interfaces.

• Incredibly low thermal conductivity (far below the amorphous limit) in the disordered, layered crystal WSe2.

– Combination of disorder (random stacking of sheets) and anisotropy (large differences in vibrations within and across the sheets) appears to be the key

– Can we reproduce this physics in materials with good electrical conductivity for thermoelectric energy conversion?

– Can we reproduce this physics in refractory oxides for thermal barriers?